The Forward Integral and Applications
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Giulia Di Nunno Bernt Øksendal Frank Proske
Malliavin Calculus for Lévy Processes with Applications to Finance
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For further volumes: http://www.springer.com/series/223
Giulia Di Nunno · Bernt Øksendal Frank Proske
Malliavin Calculus for L´evy Processes with Applications to Finance
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Giulia Di Nunno Bernt Øksendal Frank Proske Department of Mathematics University of Oslo 0316 Oslo Blindern Norway [email protected] [email protected] [email protected]
ISBN 978-3-540-78571-2 e-ISBN 978-3-540-78572-9 DOI 10.1007/978-3-540-78572-9 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2009934515 Mathematics Subject Classification (2000): 60H05, 60H07, 60H40, 91B28, 93E20, 60G51, 60G57 ¤ Springer-Verlag Berlin Heidelberg 2009, Corrected 2nd printing 2009 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH, Heidelberg The cover design is based on a graph provided by F.E. Benth, M. Groth, and O. Wallin Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To Christian. To my parents. G.D.N. To Eva. B.Ø. To Simone, Paulina and Siegfried. F.P.
Preface
There are already several excellent books on Malliavin calculus. However, most of them deal only with the theory of Malliavin calculus for Brownian motion, with [35] as an honorable exception. Moreover, most of them discuss only the application to regularity results for solutions of SDEs, as this was the original motivation when Paul Malliavin introduced the infinite-dimensional calculus in 1978 in [158]. In the recent years, Malliavin calculus has found many applications in stochastic control and within finance. At the same time, L´evy processes have become important in financial modeling. In view of this, we have seen the need for a book that deals with Malliavin calculus for L´evy processes in general, not just Brownian motion, and that presents some of the most important and recent applications to finance. It is the purpose of this book to try to fill this need. In this monograph we present a general Malliavin calculus for L´evy processes, covering both the Brownian motion case and the pure jump martingale case via Poisson random measures, and also some combination of t
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